Question

Find the set of values of x satisfying [sin x] + [cos x] = 1, ∀ x ∈ [0, 2π] 

Answer 1

When [sin x] = 0, then [cosx] = 1

⇒ x = 0, π, 2π and x = 0, 2π

⇒ x = 0, 2π

Also, when [cos x] = 0, then = [sin x] = 1

⇒ x = π/2 and x = π/2

⇒ x = π/2

Thus, the solution set is {0, π/2, 2π}